document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998073>Question 998073</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the first eight terms of an A.P. is 4 and the sum of the first twelve terms is 78.  Find the sum of the first 30 terms. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615936 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=615936\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  The sum of the first eight terms of an A.P. is 4 and the sum of the first twelve terms is 78. Find the sum of the first 30 terms. <BR>\n" );
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document.write( "1st 8 terms:: 4[a(1)+a(1)+3d] = 8a(1) + 12d = 4<BR>\n" );
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document.write( "1st 12 terms: 6[a(1)+a(1)+11d] = 12a(1)+ 66d = 78<BR>\n" );
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document.write( "Multiply thru the 1st equation by (3/2) to get::<BR>\n" );
document.write( "12a(1) + 18d = 6<BR>\n" );
document.write( "12a(1) + 66d = 78<BR>\n" );
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document.write( "48d = 72<BR>\n" );
document.write( "d = 3/2<BR>\n" );
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document.write( "Solve for \"a(1)\"::<BR>\n" );
document.write( "8a(1) + 18d = 4<BR>\n" );
document.write( "8a(1) + 27 = 4<BR>\n" );
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document.write( "8a(1) = -23<BR>\n" );
document.write( "a(1) = -23/8<BR>\n" );
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document.write( "Ans: S(30) = 15[(-23/8) + [-23/8+19(3/2)]] = <BR>\n" );
document.write( "Do the arithmetic.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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